In the prior art, arithmetic operations on analog input signals are typically performed either in the (1) original analog domain or in the (2) digital domain after an ADC conversion. In the analog domain the disadvantage is that accuracy is limited by dynamic range of the analog adding components such as analog adders. In the digital domain the disadvantage is that speed is limited by the performance of ADC conversion. Previous work on arithmetic operations on pulse type signals have been limited to methods based on stochastic logic. See J. Keane and L. Atlas, “Impulses and Stochastic Arithmetic for Signal Processing,” 2001. Methods based on stochastic logic are also limited in accuracy and in convergence speeds.
The circuit of the invention avoids the accuracy limitation of the analog computing, the speed limitation of the ADC conversion, and the speed and accuracy limitations of pulse stochastic logic. Assuming ideal elements the new circuit converges to the exact solution. The circuit is very compact and fast. The key circuit components are simple, intrinsically-linear, 1-bit digital to analog converters.
FIG. 1 shows a diagram of a prior art time encoder. This circuit has a single analog input and a single pulse output. This circuit encodes analog input signals into pulse domain signals. If the analog signal is bandlimited the encoding can be without loss of information. That is, the input u(t) can be recovered from the timing of the output signal z(t).
Preferred embodiments of the invention utilize Individual Time Encoder Circuits, which are known, per se, in the prior art and have been used before to time-encode a single analog signal input into a signal pulse output with no attempt to perform another function such as arithmetic operations. See A. Lazar and L Toth, “Perfect Recovery and Sensitivity Analysis of Time Encoded Bandlimited Signals,” IEEE Trans. on Circuits and Systems—I, vol. 51, no. 10, pp. 2060-2073, October 2004.